International Journal of Mathematical Archive-7(3), 2016,
101-107
Available online throug
ISSN 2229 – 5046
MATHEMATICS IN THIRUKKUAL
M. VINAYAGAMURTHI
M.Phil Research Scholar Of Mathematics, SCSVMV University, Kanchipuram, India.
T. N. KAVITHA*
Assistant Prof. Of Mathematics, SCSVMV University, Kanchipuram, India.
(Received On: 03-03-16; Revised & Accepted On: 25-03-16)
ABSTRACT
I
n this paper, we find the rank correlation coefficient between the knowledge about chapters of thirukkural, on according to the data collected from 1330 people opinion. Thiruvalluvar is a legend, we try to find uniformity of people opinion by chapter wise, and we collect the data about the knowable number of kurals by chapters from 1330 educated people, The chapters aram, porul, inbam and usages of this kurals by the people are different but all the people we met are used atleast one kural in their everyday work. We collect those details for our research. Some of them use the same kurals that uniformity we collect separately as numbers. So we gather the number of kurals people like the same by chapter wise, and find the rank correlation coefficient between the usage of kurals by chapters Aram, Porul and Inbum.Key words: Thirukkural, Arathupal, Porutpal, Inbathupal, Oru, Iru, rank correlation coefficient.
1. INTRODUCTION
Thirukkural was a famous literary classical work written by the great poet Thiruvalluvar over 2500 years ago. It has 1330 couplets under 133 chapters, each chapter contains 10 verses. The 133 chapters are divided into 3 major divisions. The first one is ‘ARAM’, that is ‘VIRTUE’, it contains 38 chapters. The second one is ‘PORUL’, called ‘WEALTH’. It comprises 70 chapters. The last chapter called ‘INBAM’, and it is about ‘LOVE’. It contains 25chapters.
After The Bible, Thirukkural is the only work, which has been translated in many languages. This fact tells the widely acceptances of this work by the people all over the world.
When we are scrutinizing all the couplets, we find the numbers 1, 2, 3, 4, 5, 6, 7, 8, 10, 100, CRORE, 10 CRORE, 70 CRORE and MANY CRORE in Thirukkural.
In this work we find the rank correlation coefficient between the most used (numbers) of kural by the people of Tamilnadu by chapters, Arathupal, Porutpal and Inbathupal. Here we are surprised of it, maximum of people knows atleast satisfied number of kurals and each chapters are with equal correlation.
2. USAGE OF NUMBERS IN THIRUKKURAL
In the overall 1330 kurals 14 number names are only used by Thiruvalluvar.
When we are scrutinizing all the couplets, we find the numbers 1, 2, 3, 4, 5, 6, 7, 8, 10, 100, CRORE, 10 CRORE, 70 CRORE and MANY CRORE in Thirukkural.
3. NUMERICAL FORM OF PEOPLE KNOWLEDGE ABOUT THIRUKKURAL
We collect the data from 1330 educated people, who uses the kural in their real life, and how many numbers of kurals they know. Some of the people know the similar numbers of kurals the repetition numbers we are classified, we try to find the uniformity of the knowable number of kural with the same total in chapter wise. The result, gives us the report no correlation between each chapters by the collection of data.
Corresponding Author: T. N. Kavitha*
4. THE DATA ANALYSIS OF NUMERALS
The educated people we met are at least know 312 kurals and at most they know 598 numbers of kural. So we can analyze by the number of kurals from 300 to 600 how many of them can know the same number of kural, but not the same kural. The table is below shows that:
Number of kural people know (from - to)
No Of people
300 – 320 1 321 – 340 5 341 - 360 8
361 - 380 17 381 - 400 19 401 - 420 20 421 - 440 20 441 - 460 20 461 - 480 20
481 - 500 20 501 - 520 20 521 - 540 18 541 - 560 15 560 - 580 8 581 - 5600 8
The people known number of kurals extended from 312 to 598. The known number of kurals is repeated more than one time.
We find the kurals by chapter wise and analyse it using the rank correlation method, any of the chapter have special than other? But our answer is no. All the chapters of kurals have the same place in our people mind.
The rank correlation between Arathuppal, Porutpal and Inbathuppal
The following table gives the opinion of people about the useage in their real life. The number people having the same opinion (about the same number of kurals) and we find it in the arathuppal porutpal and inbathuppal. We find their ranks.
People we met
Usage number of
kurals Arathuppal Porutpal Inbathuppal Rank(A) Rank(P) Rank(I)
483 19 3 12 4 165.5 218 208.5
473 18 4 10 4 194 214.5 208.5
446 17 3 8 6 165.5 207 217.5
451 17 3 10 4 165.5 214.5 208.5
422 16 5 9 2 206.5 210.5 170
466 16 2 11 3 133 217 196.5
433 15 6 5 4 213 163.5 208.5
445 15 2 10 3 133 214.5 196.5
448 15 4 6 5 194 187 214.5
460 15 4 7 5 194 202 214.5
463 15 8 4 2 217.5 143.5 170
478 15 3 10 2 165.5 214.5 170
482 15 8 7 0 217.5 202 43.5
423 14 5 7 2 206.5 202 170
441 14 3 6 5 165.5 187 214.5
420 13 3 5 5 165.5 163.5 214.5
444 13 3 6 4 165.5 187 208.5
453 13 6 5 2 213 163.5 170
457 13 6 5 2 213 163.5 170
459 13 3 8 2 165.5 207 170
472 13 3 9 1 165.5 210.5 119
480 13 4 6 3 194 187 196.5
425 12 3 5 4 165.5 163.5 208.5
437 12 6 4 2 213 143.5 170
438 12 4 5 3 194 163.5 196.5
439 12 5 3 4 206.5 124.5 208.5
455 12 4 7 1 194 202 119
462 12 3 7 2 165.5 202 170
465 12 0 6 6 30 187 217.5
411 11 6 3 2 213 124.5 170
421 11 4 4 3 194 143.5 196.5
426 11 3 5 3 165.5 163.5 196.5
434 11 4 4 3 194 143.5 196.5
449 11 4 4 3 194 143.5 196.5
471 11 5 5 1 206.5 163.5 119
474 11 6 3 2 213 124.5 170
475 11 6 5 0 213 163.5 43.5
490 11 4 6 1 194 187 119
410 10 3 6 1 165.5 187 119
432 10 4 6 0 194 187 43.5
435 10 3 6 1 165.5 187 119
436 10 2 7 2 133 202 170
443 10 5 5 0 206.5 163.5 43.5
464 10 1 8 1 89.5 207 119
468 10 2 6 2 133 187 170
470 10 1 9 0 89.5 210.5 43.5
484 10 3 5 2 165.5 163.5 170
488 10 3 5 2 165.5 163.5 170
492 10 3 4 3 165.5 143.5 196.5
501 10 1 6 3 89.5 187 196.5
516 10 3 6 1 165.5 187 119
412 9 3 5 1 165.5 163.5 119
430 9 3 6 0 165.5 187 43.5
442 9 2 6 1 133 187 119
447 9 1 6 2 89.5 187 170
452 9 2 4 3 133 143.5 196.5
454 9 4 3 2 194 124.5 170
479 9 1 6 2 89.5 187 170
486 9 3 5 1 165.5 163.5 119
487 9 3 5 1 165.5 163.5 119
511 9 0 9 0 30 210.5 43.5
405 8 2 5 1 133 163.5 119
408 8 4 2 2 194 95.5 170
413 8 2 4 2 133 143.5 170
414 8 3 3 2 165.5 124.5 170
415 8 2 6 0 133 187 43.5
416 8 2 4 2 133 143.5 170
417 8 2 5 1 133 163.5 119
418 8 2 5 1 133 163.5 119
419 8 1 7 0 89.5 202 43.5
429 8 0 4 4 30 143.5 208.5
456 8 1 6 1 89.5 187 119
458 8 1 6 1 89.5 187 119
461 8 3 5 0 165.5 163.5 43.5
493 8 4 2 2 194 95.5 170
502 8 5 3 0 206.5 124.5 43.5
391 7 3 3 1 165.5 124.5 119
396 7 2 4 1 133 143.5 119
397 7 1 5 1 89.5 163.5 119
401 7 4 1 2 194 54.5 170
406 7 1 3 3 89.5 124.5 196.5
427 7 3 2 2 165.5 95.5 170
431 7 4 3 0 194 124.5 43.5
450 7 1 4 2 89.5 143.5 170
481 7 0 6 1 30 187 119
485 7 1 3 3 89.5 124.5 196.5
509 7 1 6 0 89.5 187 43.5
514 7 1 5 1 89.5 163.5 119
522 7 0 5 2 30 163.5 170
523 7 1 5 1 89.5 163.5 119
381 6 3 2 1 165.5 95.5 119
389 6 1 4 1 89.5 143.5 119
390 6 2 4 0 133 143.5 43.5
424 6 3 2 1 165.5 95.5 119
428 6 1 3 2 89.5 124.5 170
476 6 3 3 0 165.5 124.5 43.5
491 6 0 3 3 30 124.5 196.5
497 6 3 2 1 165.5 95.5 119
498 6 3 2 1 165.5 95.5 119
504 6 0 6 0 30 187 43.5
506 6 1 3 2 89.5 124.5 170
513 6 3 2 1 165.5 95.5 119
542 6 3 2 1 165.5 95.5 119
394 5 0 3 2 30 124.5 170
403 5 1 2 2 89.5 95.5 170
409 5 1 2 2 89.5 95.5 170
494 5 2 2 1 133 95.5 119
495 5 4 0 1 194 16 119
496 5 2 0 3 133 16 196.5
499 5 0 4 1 30 143.5 119
503 5 0 5 0 30 163.5 43.5
517 5 3 1 1 165.5 54.5 119
518 5 1 2 2 89.5 95.5 170
525 5 2 2 1 133 95.5 119
545 5 3 2 0 165.5 95.5 43.5
357 4 0 3 1 30 124.5 119
375 4 1 2 1 89.5 95.5 119
379 4 1 2 1 89.5 95.5 119
395 4 2 0 2 133 16 170
398 4 1 2 1 89.5 95.5 119
399 4 1 2 1 89.5 95.5 119
402 4 1 2 1 89.5 95.5 119
505 4 3 1 0 165.5 54.5 43.5
508 4 2 1 1 133 54.5 119
510 4 1 3 0 89.5 124.5 43.5
519 4 4 0 0 194 16 43.5
520 4 1 3 0 89.5 124.5 43.5
526 4 0 4 0 30 143.5 43.5
533 4 2 1 1 133 54.5 119
537 4 1 2 1 89.5 95.5 119
543 4 1 3 0 89.5 124.5 43.5
551 4 3 1 0 165.5 54.5 43.5
352 3 2 1 0 133 54.5 43.5
361 3 0 1 2 30 54.5 170
362 3 1 1 1 89.5 54.5 119
363 3 1 1 1 89.5 54.5 119
364 3 1 2 0 89.5 95.5 43.5
376 3 0 1 2 30 54.5 170
380 3 0 2 1 30 95.5 119
383 3 3 0 0 165.5 16 43.5
385 3 0 2 1 30 95.5 119
386 3 0 2 1 30 95.5 119
393 3 2 1 0 133 54.5 43.5
404 3 0 2 1 30 95.5 119
407 3 0 3 0 30 124.5 43.5
500 3 2 0 1 133 16 119
524 3 1 2 0 89.5 95.5 43.5
529 3 1 1 1 89.5 54.5 119
558 3 0 3 0 30 124.5 43.5
562 3 2 1 0 133 54.5 43.5
337 2 1 1 0 89.5 54.5 43.5
340 2 0 2 0 30 95.5 43.5
367 2 1 0 1 89.5 16 119
368 2 0 1 1 30 54.5 119
374 2 0 1 1 30 54.5 119
388 2 0 2 0 30 95.5 43.5
400 2 0 2 0 30 95.5 43.5
489 2 1 1 0 89.5 54.5 43.5
507 2 0 1 1 30 54.5 119
512 2 0 1 1 30 54.5 119
521 2 1 1 0 89.5 54.5 43.5
527 2 1 0 1 89.5 16 119
528 2 0 2 0 30 95.5 43.5
535 2 1 1 0 89.5 54.5 43.5
538 2 1 0 1 89.5 16 119
549 2 0 2 0 30 95.5 43.5
550 2 0 2 0 30 95.5 43.5
554 2 1 1 0 89.5 54.5 43.5
561 2 0 2 0 30 95.5 43.5
564 2 1 1 0 89.5 54.5 43.5
578 2 1 1 0 89.5 54.5 43.5
583 2 2 0 0 133 16 43.5
312 1 0 0 1 30 16 119
330 1 1 0 0 89.5 16 43.5
331 1 1 0 0 89.5 16 43.5
338 1 1 0 0 89.5 16 43.5
342 1 0 1 0 30 54.5 43.5
350 1 0 1 0 30 54.5 43.5
354 1 1 0 0 89.5 16 43.5
355 1 0 1 0 30 54.5 43.5
358 1 1 0 0 89.5 16 43.5
359 1 1 0 0 89.5 16 43.5
365 1 0 1 0 30 54.5 43.5
366 1 0 1 0 30 54.5 43.5
370 1 0 1 0 30 54.5 43.5
373 1 1 0 0 89.5 16 43.5
377 1 0 0 1 30 16 119
378 1 0 0 1 30 16 119
384 1 1 0 0 89.5 16 43.5
387 1 1 0 0 89.5 16 43.5
392 1 0 1 0 30 54.5 43.5
515 1 0 1 0 30 54.5 43.5
530 1 0 1 0 30 54.5 43.5
531 1 0 1 0 30 54.5 43.5
534 1 0 1 0 30 54.5 43.5
536 1 0 1 0 30 54.5 43.5
539 1 0 0 1 30 16 119
541 1 1 0 0 89.5 16 43.5
544 1 0 1 0 30 54.5 43.5
548 1 0 0 1 30 16 119
553 1 0 1 0 30 54.5 43.5
556 1 0 1 0 30 54.5 43.5
559 1 1 0 0 89.5 16 43.5
560 1 0 1 0 30 54.5 43.5
565 1 0 1 0 30 54.5 43.5
567 1 1 0 0 89.5 16 43.5
569 1 0 0 1 30 16 119
579 1 1 0 0 89.5 16 43.5
581 1 1 0 0 89.5 16 43.5
582 1 0 1 0 30 54.5 43.5
585 1 0 1 0 30 54.5 43.5
590 1 0 1 0 30 54.5 43.5
593 1 1 0 0 89.5 16 43.5
598 1 0 1 0 30 54.5 43.5
Considering the orders corresponding to two characteristics Arathupal, Porutpal or Porutpal, Inbathupal and Arathupal, Inbathupal the correlation between these 218 pairs of ranks is called the rank correlation in this two characteristics.
The Karl Pearson’s formula for calculating rank correlation is developed on the assumption that the values of the variables are exactly measurable.
When the values of arathupal (A) and porutpal (P), Inbathupal (I) are find, we can rank the values in each of the variables and determine the Spearman’s rank correlation coefficient. If two or more observation have the same rank we assign to them the mean rank. In this case, there is a correlation factor in the formula for ρ. The formula for ρ is given by,
ρ = 1 -
2 2
2
(
1)
6
12
(
1)
m m
d
n n
Σ
−
Σ +
−
Therefore the repeated number of ranks can be calculated to find the rank correlation. The rank correlation between arathupal and porutpal
ΡAP = 1 -
]
[
]
2
2
6
41928.5 17900
6 949277 59828.5
1
218(218
1)
10360014
d
Σ +
+
+
= −
−
= 1- 0.58442 = 0.41558The rank correlation between porutpal and inbathupal
ΡPI = 1 -
]
22
6
17900 80483
6(855228 98383)
1
218(218
1)
10360014
d
Σ +
+
+
= −
−
= 1- 0.55228 = 0.44772The rank correlation between arathupal and inbathupal
ΡAI = 1 -
]
[
2
2
6
80483 41928.5
6 941784 122411.5]
1
218(218
1)
10360014
d
Σ +
+
+
= −
−
= 1 - 0.61633 = 0.38367Since the rank correlation coefficient between porutpal and inbathupal is positive and highest among the three chapters, porutpal and inbathupal have the nearest approach from people of Tamilnadu. Also it is not much difference between the another two.
REFERENCES
1. H. P. Blavatsky, 1880.. The Number Seven. Theosophist, June, 1880. Available online at the following links:http://theosophy.org/tlodocs/hpb/NumberSeven.htm, http://www.blavatsky.net/blavatsky/arts/NumberSe ven.htm
2. Bullinger, E.W. 1921. Number in Scripture: Its Supernatural Design and Spiritual Significance, Kregel Publications, Grand Rapids, Michigan, p. 158. The entire book is also available online at http:// philologos.org/__eb-nis/ and at http://www.levendwater.org/ boeken/numbers/ frameset.htm?index. html & inhoudsopgave.htm.
3. Raghavan Iyer, 1985. Seven Deadly Sins: The Historical Context. Hermes, November 1985. http:// theosophy.org / tlodocs/SevenDeadlySins-1.htm
4. Subbu Reddiyar, N. 1990. Science in Tamil: Then and Now. International Institute of Tamil Studies, Madras. Pp68-69.
5. Vedavyas, 1998. The concise text book of Vedic Hinduism. University of Vedic Sciences, Hyderabad, India. 330 pages
6. Hamdy A. Taha , Operations research, Eighth edition-2008. 7. Thiruvalluvar, Thirukkural.
Source of support: Nil, Conflict of interest: None Declared
